The present invention relates to control systems for dynamic systems and more specifically to adaptive control systems for an aircraft or, more generally, a flight vehicle.
Feedback control systems are used to control and improve stability of many physical systems such as flight vehicles. Conventional feedback controls are typically designed using a set of constant-value control gains. As a physical system operates over a wide range of operating conditions, the values of the control gains are scheduled as a function of system parameters. This standard approach is known as gain-scheduled feedback control. A conventional feedback control system generally requires a full knowledge of a physical system for which the control system is designed. Under off-nominal operating conditions when a system experiences failures, damage, degradation, or otherwise adverse events, a conventional feedback control system may no longer be effective in maintaining performance and stability of the system.
Adaptive control has been developed to provide a mechanism for changing control gains on line by adaptation to the system uncertainty. Thus, one advantage of adaptive control is its ability to control a physical system that undergoes significant, but unknown changes in the system behaviors. The ability to adjust control gains online makes adaptive control an attractive technology that has been receiving a lot of interests in the industry. Yet, despite the potential benefits, adaptive control has not been accepted as a mature technology which can be readily certified for deployment in mission-critical, safety-critical or human-rated systems such as aircraft flight control systems. A number of challenges presently exist such as the following:
One of problem that has not been well addressed is the adverse effect of persistent excitation. In a nutshell, persistent excitation is a condition that relates to the richness of input signals to a control system. During adaptation, some degree of persistent excitation must exist in an input signal to enable a human operator or an adaptive control system to learn and adapt to the changing environment. However, an excessive degree of persistent excitation can adversely affect stability of the system. The possibility of excessive persistent excitation can exist in off-nominal systems with human operators in the loop who sometimes can unknowingly create persistently exciting large input signal in order to rapidly adapt to the changing environment.
Another important problem that exists in adaptive control is the complex nature of the input-output signals, which are inherently nonlinear. The complex, nonlinear input-output mapping of many adaptive control methods can lead to an unpredictable behavior of a control system. To this extent, an operator cannot learn from a past response to predict what a future response will be. In contrast, a linear input-output mapping is highly desirable since the knowledge from a past response can be used to predict a future response. Consequently, adaptive control systems tend to be unpredictable and inconsistent in their behaviors. The predictability of a control system is a crucial element in the operation of a control system that involves a human operator such as an aircraft pilot or an automobile driver. Unpredictability can result in over-actuated or under-actuated control signals which both can lead to undesirable outcomes and potentially catastrophic consequences.
The sensitivity of adaptive control systems to large inputs and persistent learning is another important consideration. Because of the nonlinear behaviors, large inputs can lead to deleterious effects on adaptive control systems. A physical system may be stable when small amplitude inputs are used in adaptive control, but the same system can become unstable when the input amplitude increases. The amplitude of an input can be difficult to control because it can be generated by a human operator like a pilot. Persistent learning is referred to the process of constant adaptation to small error signals. In some situations, when an adaptive control system has achieved sufficient performance, the adaptation process needs to be scaled down. Maintaining a constant state of fast adaptation even after the errors have diminished can result in persistent learning. At best, persistent learning would do nothing to further improve the performance. At worst, persistent learning reduces robustness of an adaptive control system by constantly adapting to small error signals.
The most fundamental issue is the lack of metrics to assess stability of an adaptive control system. Currently, there are no well-established metrics or methods for analyzing thereof that can satisfy conventional certification requirements for adaptive control. Unlike conventional classical linear control which is endowed with many important and useful tools for analyzing performance and stability certification requirements of a closed-loop system, adaptive control suffers a disadvantage of the lack thereof. Consequently, there is currently no fielded adaptive control system certified for use in any production system.
A distinct feature of a typical adaptive control design is the ad-hoc, trial-and-error nature of the design process which involves selecting suitable design parameters such as the adaptive gain, or adaptation rate, without analytical methods for guiding the design. A trial-and-error design process may enable an adaptive control system to work well under a design conditions, but by the same token may fail to work well under other conditions. As a result, this ad-hoc process tends to make the design of adaptive control to be particularly difficult to implement by general practitioners of control systems.
There exist several robust modification adaptive control methods. The two most popular conventional methods are the σ-modification and the e-modification. Both or these methods were established in the 1980's. The σ-modification adaptive control provides a constant damping mechanism to limit the adaptation process from becoming unstable, and the e-modification provides a damping mechanism that is proportional to the norm of the tracking error signal to accomplish the same. The projection method is another popular method that is used to bound adaptive parameters to prevent issues with persistent learning. As with most adaptive control methods, the aforementioned challenges exist in one form or another.